A Huff model with firm heterogeneity and selection. Application to the Italian retail sector

ABSTRACT

In this paper, firm heterogeneity (in terms of productivity, i.e., marginal costs) is incorporated into a Huff model of competition in the Italian retail sector. A higher market potential in the trade area is associated with higher average productivity and lower productivity dispersion through selection of the best stores. The analysis, based on a unique data set encompassing 14,212 Italian retailers, finds support for this relationship in Southern Italy, but not in Northern and Central Italy (where opposite results are obtained in some cases), suggesting the selection dynamics are affected by context factors (other than provincial/regional accessibility) related to an upper geographical scale. The results are robust to controlling for local context factors such as financial risk and floor size restrictions. Floor size restrictions are found to enhance selection.

KEYWORDS:

• Huff model
• firm selection
• accessibility
• trade areas
• retail location

JEL:

• F12
• L81
• R3
• R12

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

SUPPLEMENTAL DATA

Supplemental data for this article can be accessed at https://doi.org/10.1080/17421772.2018.1451914.

ORCID

Massimo Del Gatto http://orcid.org/0000-0002-3261-8038

Notes

1 The expression ‘New Trade Theory’ was coined to refer to a strand of international trade literature, pioneered by Krugman (1980) and further developed by Dixit and Norman (1980), Markusen (1981), Helpman (1984) and Helpman and Krugman (1985), among others, that focused on the role of increasing returns to scale and imperfect competition in international trade. While New Trade models successfully explained some key facts in international trade, such as the emergence of intra-industry flows, subsequent literature highlighted additional competition effects: higher competition forces the least productive firms to leave the market (Aw, Chung, & Roberts, 2000; Bernard & Jensen, 1999; Clerides, Lach, & Tybout, 1998) and induces market-share reallocations towards the more productive firms (Bernard, Jensen, & Schott, 2006; Pavcnik, 2002). Recent theoretical literature accommodated this ‘selection effect’ by enriching the New Trade Theory approach with the assumption that firms are heterogeneous in terms of productivity (i.e., total factor productivity). This generated the class of models (i.e., Bernard, Eaton, Jensen, & Kortum, 2003; Melitz, 2003; Melitz & Ottaviano, 2008) referred to as ‘New New Trade Theory’.

2 The productivity of firms that generate revenues barely sufficient to cover costs defines the threshold below which it is impossible for a firm to survive in the market. This threshold of survival determines the average productivity of active firms.

3 The demand function in equation (1) is based on the assumption that the probability that consumer , confronted with a set of alternatives, will select a given store is directly proportional to the perceived utility of each alternative. The choice is probabilistic, and each store is characterized by a positive probability:to be chosen, where is the consumer’s utility associated with choice (and ). Assuming that is directly proportional to and inversely proportional to , with the degree of proportionality expressed by the two parameters and , it yields the demand function in equation (1). Inelasticity entails that if only one store existed, the total number of consumers would patronize it regardless of where it is located.

4 Alternatively, one can imagine production also to require labour, with the latter inelastically provided by consumers at unit wage (i.e., ).

5 Given the one-to-one relationship between UIR and size, the equilibrium UIR no longer depends on size, once equation (4) is used to substitute for into equation (5).

6 The condition allows the integral in equation (5) to converge to a meaningful solution.

7 The simplest measure of dispersion would be the ‘range’, defined as the UIR gap between the best- and worst-performing stores. However, given the support , the range is simply equal to , so it increases with the degree of competition in the trade area. While easily understood, being based on the two boundary values only, the range is necessarily very sensitive to extreme observations and should be used together with other measures. The SD is the most widely used measure of dispersion. Although less sensitive, the SD might also be problematic in highly skewed distributions. The Appendix in the supplemental data online provides robustness checks for both average and dispersion by relying on the median and the interquartile range.

8 In principle, one might want to go deeper into the geographical disaggregation and estimate region-specific AMUSA effects and UIR distributions. Although we explore this dimension in the Appendix in the supplemental data online, this exercise is beyond the scope of the present benchmark analysis. Since we are concerned with providing ‘general results’ concerning the effectiveness of the selection effect, the analysis requires detailed data, on the one hand, as the reference unit is the retail trade area, and a wide geographical scale, on the other hand, in order to avoid results that are too specific. Moreover, a higher number of observations would be needed in order to obtain consistent estimates at a regional level. This is particularly true in the dispersion analysis, where the number of observations shrinks considerably because of the municipalities in which only one store is observed (Tables 1 and 2).

9 See: http://www.nielsen.com/.

10 Simultaneity arises because information on , although unknown to the econometrician, is commonly used by the firm in its decision concerning the amount of inputs. This issue makes the error term in the estimation correlated with capital and labour, and the ordinary least squares (OLS)-estimated biased. The solution suggested by Olley and Pakes (1996) exploits the idea that investment (i.e., the ‘proxy variable’) reacts to the changes in observed by the firm and is, therefore, a function of it. Under reasonable assumptions, this function is invertible and its inverse can be plugged into the estimating equation before proceeding to estimate the production function parameters (Del Gatto, Di Liberto, & Petraglia, 2011; Van Beveren, 2012). Although we use ours, the Olley–Pakes routine is implemented in Stata under the command ‘opreg’ (Yasar, Raciborski, & Poi, 2008).

11 The production function , stated in the next section, is nested in this standard specification as far as stores’ sales area is included in the book value of capital.

12 In the case of multi-store firms, the UIR refers to the main branch.

13 The resulting OD matrix underestimates actual travel times, for different reasons. First, the data only include extra-urban roads, so we do not consider the time required to reach the extra-urban road network. Second, the analysis excludes any kind of barriers (such as traffic lights and toll gates). Third, we use the maximum allowed speed as the reference speed of travel.

14 See www.immobiliare.it/.

15 As noticed by Schivardi and Viviano (2011), the Italian retail sector, which has a prevalence of traditional small stores, underwent a major regulatory change in 1998. A central feature of the new law is that it delegates the regulation of entry of medium-to-large stores into local authorities. As it turns out, local regulations differ substantially in their approach to competition: in particular, most regions have established stringent ceilings to the floor space that can be authorized for the entry of medium-to-large stores at the local level.

16 The number of observations differs across the two sets of regressions owing to the presence of municipalities exhibiting zero dispersion (only one store observed), turning into missing in the log estimation.

17 The ESPON accessibility measures used in Table 2 are province-level (upper panel) and region-level (bottom panel) variables computed on 2006 data. The accessibility of province/region is defined as:where is the aggregation, over transport modes (i.e., air, rail, road), of the cost () of reaching  from using transportation mode , i.e.:where is the gross domestic product-purchasing power standard (GDP-PPS) per capita and population in region respectively for the two measures computed at the province and region levels; and is a parameter indicating the sensitivity to travel cost. The interpretation is that the accessibility of increases with the number of ‘accessible’ provinces/regions and with their size (either GDP or population).

18 In this case, we do not divide by .

Additional information

Funding

The authors gratefully acknowledge financial support from the Analisi dei costi economici addizionali attribuibili allo stato di insularità, con particolare riferimento alla di differenza rispetto a casi di ‘geographic remoteness’ riconosciuti nellambito della politica regionale europea, a project of European interest funded by the local government of the Sardinia region of Italy.